Mathematics and physics are entirely different subjects, both in their methodology and results. The differences are illustrated with how they view randomness, enumeration, and truth. In physics, randomness can be an unknown, an observational error, an unpredictable event, or a quantum mystery. In math it is just part of probability theory. Mathematics has subtle properties of infinities that physics does not directly observe. Logical positivism is a philosophy that explains how mathematics and physics search for truth in different ways, but it has been rejected by modern philosophers, leaving them with deeply flawed views of what math and physics are all about.
Roger Schlafly